diff --git a/Cat_UG_00/cat_ug.pdf b/Cat_UG_00/cat_ug.pdf
index e0b5abfa052065778bc25bae76ef8efa88bdc216..db104446bd4f258cd645d56e05395ec9d43e823c 100644
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diff --git a/Cat_UG_00/chap_evoleq.tex b/Cat_UG_00/chap_evoleq.tex
index 12305becf9fc6d36d9413c2740efda781081a17d..567c07980ed8da9c118f4a3d5b96b56570cb2113 100644
--- a/Cat_UG_00/chap_evoleq.tex
+++ b/Cat_UG_00/chap_evoleq.tex
@@ -1,4 +1,4 @@
-%
+
\chapter{Evolution equations of incompressible 2D fluids}
%
%
@@ -20,7 +20,7 @@ From homogeneity and incompressibility of the fluid we get
\rho \mathbf{\nabla \cdot u} = 0,
\end{equation}
with $\rho$ the fluid density. Using this property we can introduce
-a volume (mass) stream function measuring the volume (mass) flux
+a volume (mass) streamfunction measuring the volume (mass) flux
across an arbitrary line from the point $(x_{0},y_{0})$ to a point $(x,y)$
via the path integral
\begin{equation} \label{eq_psizetadef}
@@ -45,10 +45,10 @@ via the path integral
\end{equation}
The minus sign in front of the integral just changes the direction
of positive massflux across the line and is chosen to make
-the classical stream function of 2D fluids compatible to
-the stream function (see e.g.\ \cite{danilovandgurarie2000})
+the classical streamfunction of 2D fluids compatible to
+the streamfunction (see e.g.\ \cite{danilovandgurarie2000})
typically used for 2D rotating fluids in geosciences.
-In terms of the stream function $\psi$ the integrated mass flux
+In terms of the streamfunction $\psi$ the integrated mass flux
$\mathcal{M}$ across a line joining the points $(x_{0},y_{0})$ and
$(x,y)$ is given by
\begin{equation} \label{eq_calM}
@@ -57,109 +57,235 @@ $(x,y)$ is given by
\left[\psi(x,y) - \psi(x_{0},y_{0}) \right],
\end{equation}
with $H_{0}$ the depth of the fluid. At the same time
-the stream function $\psi$ is connected to the velocity
+the streamfunction $\psi$ is connected to the velocity
field $(u,v)$ and the (relative)
vorticity $\zeta = v_{x} - u_{y}$ via
\begin{equation} \label{eq_psiuv}
(u,v) = (- \psi_{y},\psi_{x}) \ \mbox{and} \ \ \zeta = \Delta \psi.
\end{equation}
-Using the stream function $\psi$, the evolution equation (\ref{eq_2Dvortvel}
-can be also written in the form
+Using the streamfunction $\psi$, the evolution equation (\ref{eq_2Dvortvel})
+can be written in the form
\begin{equation} \label{eq_2Dvortstream}
- \zeta_{t} + J(\psi,\zeta) = F + D.
+ \zeta_{t} + J(\psi,\zeta) = F + D,
\end{equation}
+with $J(\psi,\zeta) = \psi_{x} \zeta_{y} - \psi_{y} \zeta_{x}$ the Jacobian.
Since the velocity field is divergence free (equation \ref{eq_conti})
-we can further derive the equivalent equation in flux form
+different representations of the Jacobian $J$ can be found. Using
+appropriate superpositions of different representations one can derive
+discrete analogs of the Jacobian $J$ which keep the symmetry
+property $J(\psi,\zeta) = -J(\zeta,\psi)$ and conserve the integrated
+vorticity $\zeta$, kinetic energy $\nabla \psi \cdot \nabla \psi $ and
+enstrophy $\zeta^{2}$. In \cite{arakawa1966} such a discrete analog is
+derived for a finite difference numerical model. Keeping the notation of
+\cite{arakawa1966} the Jacobian $J$ of equation (\ref{eq_2Dvortstream})
+is denoted by $J_{1}$. Starting from $J_{1}$ we can derive a second form
+of the Jacobian
+\begin{equation} \label{eq_Jacobi2}
+ J_{2}(\psi,\zeta)
+ =
+ J_{1}(\psi,\zeta) + \psi \left( \zeta_{xy} - \zeta_{yx} \right)
+ =
+ \left(\psi \zeta_{y} \right)_{x}
+ -
+ \left(\psi \zeta_{x} \right)_{y},
+\end{equation}
+which gives the evolution equation
+\begin{equation} \label{eq_2DJacobi2}
+ \zeta_{t} + \left(\psi \zeta_{y} \right)_{x}
+ - \left(\psi \zeta_{x} \right)_{y} = F + D.
+\end{equation}
+Further we can derive a third form of Jacobian $J_{3}$ as follows
+\begin{equation} \label{eq_Jacobi3}
+ J_{3}(\psi,\zeta)
+ =
+ J_{1}(\psi,\zeta) + \zeta \left( \psi_{xy} - \psi_{yx} \right)
+ =
+ \left(\zeta \psi_{x} \right)_{y}
+ -
+ \left(\zeta \psi_{y} \right)_{x},
+\end{equation}
+which inserted in the evolution equation yields the 2D fluid equations
+in flux form
\begin{equation} \label{eq_2Dflux}
- \zeta_{t} + \nabla \cdot \left(\mathbf{u} \zeta \right) = F + D.
+ \zeta_{t} +
+ \left(\zeta \psi_{x} \right)_{y}
+ -
+ \left(\zeta \psi_{y} \right)_{x},
+ =
+ \zeta_{t} + \nabla \cdot \left(\mathbf{u} \zeta \right)
+ = F + D.
\end{equation}
-Starting from the flux form one can after repeated application of the
-continuity equation (\ref{eq_conti}) finally derive an equation where
-the Jacobian only depends on the two velocity fields $(u,v)$
-\begin{equation} \label{eq_2Duv}
- \zeta_{t}
- + \partial_{x} \partial_{y} \left( v^{2} - u^{2} \right)
- + \left(\partial^{2}_{x} - \partial^{2}_{y} \right) uv
+It is possible to derive a fourth form of the Jacobian $J_{4}$
+which is a funciton of the field $v^{2} - u^{2})$ and
+$uv$. We start again from the first Jacobian $J_{1}$
+\begin{equation} \label{eq_Jacobi4}
+ J_{4}(\psi,\zeta)
+ =
+ J_{1}(\psi,\zeta) +
+ \left(2 \zeta - \psi_{x} \right) \ \left( \psi_{xy} - \psi_{yx} \right)
+ =
+ \left(v^{2} - u^{2} \right)_{xy}
+ +
+ \left(uv \right)_{xx-yy},
+\end{equation}
+which leads to the evolution equation
+\begin{equation} \label{eq_2DJacobi4}
+ \zeta_{t}+ \left( v^{2} - u^{2} \right)_{xy} + \left( uv \right)_{xx - yy}
=
F + D.
\end{equation}
-This form allows in the pseudo-spectral method (see \ref{sec_evolfourier})
-to reduce the number of Fourier transforms per time-step from
-$3$, i.e.\ ($u,v,\zeta$) to $2$, i.e.\ ($u,v$).
-
+All four forms given above are equivalent so that mathemtically one form is
+sufficient to catch all properties of the equations. Of course also other
+forms can be derived and it is also possible to superpose serveral forms.
+The different forms get important if one tries to find discrete
+representations of the Jacobian in the numerical scheme. Each form leads
+to a discrete representation with different conservation and symmetry
+properties. For more details see the chapters on the conservation
+properties (\ref{sec_conprops}) and on the pseudo-spectral method
+(\ref{sec_evolfourier}).
%
\section{Quasi-two-dimensional rotating case} \label{sec_quasi2Dcase}
%
Starting from the shallow water equation on the $\beta$-plane one can
derive (see e.g. \cite{danilovandgurarie2000}) an equation
describing a rotating barotropic quasi-two-dimensional fluid which is a
-generalization of the 2D-equation (\ref{eq_2Dvortvel}). For small Rossby
-numbers $\mathrm{Ro} = U/Lf$, with $U$ a typical horizontal fluid velocity
-at the length scale $L$ considered and $f$ the local coriolis paramter
-we get the potential vorticity (PV) $q$ in quasi-geostrophic (QG) approximation
+generalization of the 2D-equation (\ref{eq_2Dvortvel}). The shallow
+water potential vorticity is defined by
+\begin{equation} \label{eq_qshallow}
+ q_{s} = \frac{\zeta + f}{H},
+\end{equation}
+where $H(x,y,t)$ is the fluid depth and $f$ the planetary vorticity.
+Decomposing the fluid depth into a mean depth $H_{0}$, a constant
+bottom topography B(x,y) and a time-dependent
+depth deviation $h(x,y,t)$ we can write $H(x,y,t) = H_{0} + h(x,y,t) - B(x,y)$.
+Inserting the decomposition of the fluid depth into the equation
+(\ref{eq_qshallow}) we can expand the potential vorticity
+\begin{equation} \label{eq_qshallowdecomp}
+ q_{s}
+ =
+ \frac{\zeta + f}{H_{0} + h - B}
+ =
+ \frac{1}{H_{0}} \ \frac{\zeta + f}{1 + \Delta H / H_{0}}
+ =
+ \frac{1}{H_{0}} \
+ \left( \zeta + f \right) \left(1 - \frac{\Delta H}{H_{0}} + \dots \right),
+\end{equation}
+with $\Delta H = h - B$. Keeping only linear terms we finally get the barotopic
+vorticity
+\begin{equation} \label{eq_qbaro}
+ q = H_{0} q_{s} = \zeta - \frac{f}{H_{0}} \left(h - B\right) + f.
+\end{equation}
+Here we assume that the depth deviations $\Delta H = h - B$ are much smaller
+than the mean depth $H_{0}$. For small Rossby numbers $\mathrm{Ro} = U/Lf$,
+with $U$ a typical horizontal velocity scale, $L$ a typical horizontal
+length scale of the fluid motion and $f$ the local coriolis parameter
+we can (see again e.g.\ \cite{danilovandgurarie2000}) introduce
+the streamfunction
+\begin{equation} \label{eq_psibaro}
+ \psi(x,y,t) = \frac{g}{f} \ h(x,y,t),
+\end{equation}
+with $g$ the gravity. Using this streamfunction and expanding the
+coriolis parameter linarly we can write the barotropic
+quasi-geostrophic (QG) potential vorticity (PV)
+on the $\beta$-plane (\ref{eq_qbaro}) as
\begin{equation} \label{eq_qdef}
- q = \left( \nabla^{2}- \alpha^{2} \right) \psi + f,
+ q = \left( \nabla^{2}- \alpha^{2} \right) \psi
+ + f_{0} + \beta y + \frac{f_{0}}{H_{0}} \ B.
+\end{equation}
+The linear expansion of the Coriolis parameter
+$f(\varphi) = 2 \Omega \sin \varphi$ which is defined on a sphere
+with radius $a$ and rotation rate $\Omega$ leads to
+\begin{equation} \label{eq_fbeta}
+ f(\varphi_{0} + \Delta \varphi)
+ =
+ f(\varphi_{0}) + f^{\prime}(\varphi_{0}) \Delta \ \varphi
+ =
+ f_{0} + \beta y,
+\end{equation}
+with $\varphi_{0}$ the central latitude and the meridional
+coordinate $y = a \Delta \varphi$ which is the linearization of
+the projection $y = a \sin(\Delta \varphi)$. The $\beta$-parameter
+is defined by $\beta = 2 \Omega \cos(\varphi_{0})/a$. The modification
+parameter $\alpha = 1/L_{\mathrm{R}}$ is connected to the Rossby-Obukhov
+radius of deformation $L_{\mathrm{R}} = \sqrt{g H_{0}}/f$.
+As in the $2$-dimensional case the streamfunction $\psi$
+(remind the different definition) is related to the velocity field
+$(u,v)$ again (see also equation \ref{eq_psiuv}) via
+\begin{equation} \label{eq_upsibaro}
+ u = -\psi_{y} \ \ \ \mbox{and} \ \ \ v = \psi_{x}.
\end{equation}
-where we have the modification parameter $\alpha = 1/L^{2}_{\mathrm{R}}$
-with the Rossby-Obukhov radius of deformation
-$L_{\mathrm{R}} = \sqrt{g H_{0}}/f$ and the stream function
-$\psi = gh/f$. Here $g$ is the gravitational acceleration and $h(x,y)$
-the deviation of the mean fluid depth $H_{0}$ of the original
-shallow water layer. As in the $2$-dimensional case the stream function $\psi$
-(remind the different definition) is related to the velocity fields $(u,v)$
-as defined in equation (\ref{eq_psiuv}). In an unforced non-dissipative fluid
-the QG PV is materially conserved
+In an unforced and non-dissipative fluid the QG PV is materially conserved
\begin{equation}
q_{t} + J(\psi,q) = 0.
\end{equation}
-Using the linear approximation of the coriolis parameter $f = f_{0} + \beta y$
+Using the linear approximation of the coriolis parameter (\ref{eq_fbeta})
and introducing again forcing and dissipation we can write the evolution
-equation in the form
+equation for a barotropic fluid on the $\beta$-plane in the form
\begin{equation} \label{eq_quasi2Dbaro}
- q_{t} + J(\psi,q) + \beta \psi_{x} = F + D,
+ q_{t} + J(\psi,q + \frac{f_{0}}{H_{0}} \ B) + \beta \psi_{x} = F + D,
\end{equation}
-with the vorticity $q$ given by
+with the vorticity $q$ again given by
\begin{equation} \label{eq_vortquasi2Dbaro}
q = \left(\nabla^2 -\alpha^{2} \right) \psi
= \zeta - \alpha^{2} \psi.
\end{equation}
-Further one can introduce a variable mean fluid depth $H(x,y)$,
-which in the simple case of a linear slope in $y$-direction leads
-to a topographic $\beta$-effect (see e.g.\ \cite{vanheist1994}).
+Here we used the property of the Jacobian $J(f,f) = 0$ for all fields
+$f(x,y)$ on the fluid domain.
+Idealizing the bottom topography to a linear slope in y-direction
+$B(x,y) = B_{y} y$ the fluid experiences in addition to the ambient
+planetary $\beta$-effect a so called topographic $\beta$-effect
+(see e.g.\ \cite{vanheist1994}) and the evolution equation simplifies to
+\begin{equation} \label{eq_qbarotopobeta}
+ q_{t} + J(\psi,q) + \left(\beta + \frac{f_{0}}{H_{0}} B_{y} \right) \psi_{x}
+ = F + D.
+\end{equation}
In the form (\ref{eq_quasi2Dbaro}) and (\ref{eq_vortquasi2Dbaro})
-one can simulate incompressible 2D fluids and rotating quasi-2D fluids
-with the same set of equations using different parameters.
+one can simulate incompressible 2D fluids and rotating barotropic
+quasi-2D fluids with the same set of equations using different parameters.
In this more general frame the simplest case of a non-rotating
2D incompressible fluid is characterized by a vanishing
ambient vorticity gradient, i.e.\ $\beta = 0$, and the limit of
an infinite Rossby radius $L_{\mathrm{R}} \longrightarrow \infty$
or a vanishing modification parameter $\alpha \longrightarrow 0$.
+One has to keep in mind that the streamfunctions are different in
+the two cases (see e.g.\ \cite{johnstonandliu2004}) and that there
+are more subtle differences between 2D and QG Turbulence
+(see e.g.\ \cite{tungandorlando2003}).
+%
+\section{Multi-layer quasi-geostrophic case} \label{sec_multilayerqg}
+%
+%
+\section{The surface geostrophic case} \label{sec_sqg}
+%
+%
+\section{Conservation properties} \label{sec_conprops}
+%
+The properties of the Jacobian and the conditions at the fluid boundaries
+are at the base of the conservation properties of the fluid motions.
+Given two functions $g(x,y)$ and $h(x,y)$ defined on the fluid domains
+then the following integrals
+\begin{equation} \label{eq_intjacobian01}
+ \int_{x=0}^{X} \int_{x=0}^{Y} J(A,B) \ dxdy
+ , \
+ \int_{x=0}^{X} \int_{x=0}^{Y} A J(A,B) \ dxdy
+ \ \ \mbox{and} \ \
+ \int_{x=0}^{X} \int_{x=0}^{Y} B J(A,B) \ dxdy
+\end{equation}
+can be transformed through partial integration.
-One has to keep in mind that the stream functions are different in
-the two cases. In the non-rotating case $\psi$ is defined by
-equation (\ref{eq_calM}). In the rotating case we get
-\begin{equation} \label{eq_hquasi2Dbaropsi}
- h(x,y) = \frac{f}{g} \ \psi(x,y),
-\end{equation}
-so that $\psi$ is proportional to pressure deviations, which is not
-the case in the non-rotating 2D case where the relation is more
-complex, see e.g.\ \cite{johnstonandliu2004}.
-Using the property of the Jacobian $J(f,f) = 0$ for all fields
-$f(x,y)$ on the fluid domain, equation (\ref{eq_quasi2Dbaro})
-is equivalent to
-\begin{equation} \label{eq_quasi2Dbarozeta}
- q_{t} + J(\psi,\zeta) + \beta \psi_{x} = F + D,
-\end{equation}
-where the vorticity $q$ is still defined by equation
-(\ref{eq_vortquasi2Dbaro}). From this from it directly follows that
-that the form of the 2D Jacobian in equations
-(\ref{eq_2Dflux}) and (\ref{eq_2Duv}) can be also applied in the
-quasi-two-dimensional rotating case.
-\section{Non-adiabatic terms}
+Above results can be generalized to more general fluid domains
+(see e.g.\ \cite{salmonandtalley1989}).
+
+
+
+
+%
+\section{Non-adiabatic terms}
+%
\subsection{Laplacian based Viscosity and friction}
Internal viscosity and external friction of the fluid are described by
diff --git a/Cat_UG_00/chap_pseudospec.tex b/Cat_UG_00/chap_pseudospec.tex
index 330129dda1bf7a71169f35d37839aab187847f09..259dee39b709dc4c017d21b0fd71f616c99b1898 100644
--- a/Cat_UG_00/chap_pseudospec.tex
+++ b/Cat_UG_00/chap_pseudospec.tex
@@ -1079,11 +1079,11 @@ purely spectral and is called pseudo-spectral method, see e.g.\
the higher wave numbers have to be filtered out. In CAT trunction is
used, see above.
-We present three different forms of the Jacobian $J$ in physical space,
-see equations (\ref{eq_2Dvortstream}), (\ref{eq_2Dflux})
-and (\ref{eq_2Duv}). Using the pseudo-spectral method for each
-form we get a different representation of the Jacobian $\hat{J}$
-in spectral space.
+We present four different forms of the Jacobian $J$ in physical space,
+see equations (\ref{eq_2Dvortstream}), (\ref{eq_2Dflux}),
+(\ref{eq_2DJacobi2}) and (\ref{eq_2DJacobi4}). Using the pseudo-spectral
+method for each form we get a different representation of the
+Jacobian $\hat{J}$ in spectral space.
For the Jacobian (\ref{eq_2Dvortstream}) of the first form
\begin{equation} \label{eq_jacobian01}
@@ -1091,18 +1091,18 @@ For the Jacobian (\ref{eq_2Dvortstream}) of the first form
=
J(\psi,q)
=
- \partial_{x} \psi \ \partial_{y} q
+ \psi_{x} \ q_{y}
-
- \partial_{x} q \ \partial_{y} \psi
+ q_{x} \ \psi_{y}
=
- \left[ v \ \partial_{y} q + u \ \partial_{x} q \right],
+ v \ q_{y} + u \ q_{x},
\end{equation}
one proceeds as follows. First the individual differential terms
are determined in spectral space using the fourier transform of
vorticity, and the spectral representation of the differential
-operators. We get
+operators. The basic operators are given by
\begin{eqnarray} \label{eq_jacobian01_termsa}
- \mathcal{F}(\partial_{x} \psi)
+ \mathcal{F}(\psi_{x})
&=&
i k_{x} \ \mathcal{F}(\psi)
=
@@ -1111,11 +1111,11 @@ operators. We get
- \ i \ \frac{k_{x}}{k^{2}_{x} + k^{2}_{y} + \alpha} \
\mathcal{F}(q),
\ \
- \mathcal{F}(\partial_{y} q)
+ \mathcal{F}(q_{y})
=
i k_{y} \ \mathcal{F}(q) \ \ \
\\ \label{eq_jacobian01_termsb}
- \mathcal{F}(\partial_{y} \psi)
+ \mathcal{F}(\psi_{y})
&=&
i k_{y} \ \mathcal{F}(\psi)
=
@@ -1124,7 +1124,7 @@ operators. We get
- \ i \ \frac{k_{y}}{k^{2}_{x} + k^{2}_{y} + \alpha} \
\mathcal{F}(q),
\ \
- \mathcal{F}(\partial_{x} q)
+ \mathcal{F}(q_{x})
=
i k_{x} \ \mathcal{F}(q). \ \ \
\end{eqnarray}
@@ -1137,43 +1137,41 @@ $\hat{J}$ is given by
\begin{equation} \label{eq_jacobian01_J}
\hat{J}
=
- \mathcal{F}(v \partial_{y} q)
- -
- \mathcal{F}(u \partial_{x} q).
+ \mathcal{F}(v q_{y})
+ +
+ \mathcal{F}(u q_{x})
+ =
+ \mathcal{F}(v q_{y} + u q_{x}).
\end{equation}
Combining all necessary steps we can write
-\begin{eqnarray} \nonumber
+\begin{equation} \label{eq_jacobian01_Jall}
\hat{J}
- &=&
+ =
\mathcal{F}
- \left(
+ \left[
\mathcal{F}^{-1}
\left(
- \ - \ i \frac{k_{x}}{k^{2}_{x}+k^{2}_{y}+\alpha} \
+ - i \frac{k_{x}}{k^{2}_{x}+k^{2}_{y}+\alpha} \
\hat{q}
\right)
\mathcal{F}^{-1}
\left(
ik_{y} \ \hat{q}
\right)
- \right)
- \\ \label{eq_jacobian01_Jall}
- &-&
- \mathcal{F}
- \left(
+ +
\mathcal{F}^{-1}
\left(
- \ i \frac{k_{y}}{k^{2}_{x}+k^{2}_{y}+\alpha} \
+ i \frac{k_{y}}{k^{2}_{x}+k^{2}_{y}+\alpha} \
\hat{q}
\right)
\mathcal{F}^{-1}
\left(
ik_{x} \ \hat{q}
\right)
- \right),
-\end{eqnarray}
+ \right],
+\end{equation}
where $\hat{q}$ is the vorticity in spectral space, the starting point
-for a new time step. As can be seen one needs $6$ $2$-FFT operations
+for a new time step. As can be seen one needs $5$ $2D$-FFT operations
to determine the Jacobian. The components of the Jacobian
$\hat{J}_{k}$ are then used to determine the time
evolution of the different wave number components of the vorticity
@@ -1182,11 +1180,7 @@ $\hat{q}_{\mathbf{k}}$, see equation (\ref{eq_evolqhat}).
In the flux form of the evolution equation ({\ref{eq_2Dflux}})
the second form of the Jacobian arises
\begin{equation} \label{eq_jacobian02}
- J(\psi,q)
- =
- \partial_{x} (u \ q)
- +
- \partial_{x} (v \ q).
+ J(\psi,q) = (u \ q)_{x} + (v \ q)_{y}.
\end{equation}
Following again equations (\ref{eq_jacobian01_termsa}) and
(\ref{eq_jacobian01_termsb}) we determine $\mathcal{F}(u)$ and
@@ -1235,14 +1229,47 @@ Combining again all necessary steps we can write
As we can see the Jacobian in spectral space $\hat{J}$ can now be
determined by $5$ FFT operations.
-The third form of the Jacobian used in equation (\ref{eq_2Duv}) is
-given by
+The third form of the Jacobian in equation (\ref{eq_2DJacobi2})
+is given by
\begin{equation} \label{eq_jacobian03}
+ J(\psi,q) = (\psi \ q_{y})_{x} - (\psi \ q_{x})_{y}.
+\end{equation}
+In spectral space we get
+\begin{equation} \label{eq_jacobian03_J}
+ \hat{J} = -ik_{x} \ \mathcal{F}(\psi \ q_{y})
+ +ik_{y} \ \mathcal{F}(\psi \ q_{x}).
+\end{equation}
+Combining all necessary steps the Jacobian is determined by
+\begin{eqnarray}
+ \hat{J}
+ &=&
+ -ik_{x} \
+ \mathcal{F}\left(
+ \mathcal{F}^{-1}
+ \left(-\frac{1}{k_{x}^{2} + k_{y}^{2} + \alpha} \ \hat{q} \right) \
+ \mathcal{F}^{-1}
+ \left(
+ -ik_{y} \ \hat{q}
+ \right)
+ \right)
+ \\ \label{eq_jacobian03_Jall}
+ &+&
+ ik_{y} \
+ \mathcal{F}\left(
+ \mathcal{F}^{-1}
+ \left(-\frac{1}{k_{x}^{2} + k_{y}^{2} + \alpha} \ \hat{q} \right) \
+ \mathcal{F}^{-1}
+ \left(
+ -ik_{x} \ \hat{q}
+ \right)
+ \right).
+\end{eqnarray}
+The fourth form of the Jacobian used in equation (\ref{eq_2DJacobi4}) is \begin{equation} \label{eq_jacobian04}
J(\psi,q)
=
\partial_{x}\partial_{y} \left(v^{2} - u^{2} \right)
+
- \partial^{2}_{x} \partial^{2}_{y} uv.
+ \left( \partial^{2}_{x} - \partial^{2}_{y} \right) uv.
\end{equation}
In this representation it is possible to reduce the number of FFT
operations from $5$ to $4$. We first have to determine $\hat{u}$
@@ -1252,12 +1279,12 @@ space where the products $v^{2} - u^{2}$ and $uv$ are formed.
Finally we have to transform them back to spectral space where they
are differentiated. The Jacobian in spectral space $\hat{J}$ is
given by
-\begin{equation} \label{eq_jacobian03_J}
+\begin{equation} \label{eq_jacobian04_J}
\hat{J}
=
-k_{x}k_{y} \ \mathcal{F}(v^{2} - u^{2})
+
- k^{2}_{x}k^{2}_{y} \mathcal{F}(uv)
+ \left( k^{2}_{x} - k^{2}_{y} \right) \mathcal{F}(uv)
\end{equation}
or by combining all necessary steps
\begin{eqnarray} \nonumber
@@ -1284,7 +1311,7 @@ or by combining all necessary steps
\right)
\\ \label{eq_jacobian02_Jall}
&+&
- k^{2}_{x} k^{2}_{y} \
+ \left( k^{2}_{x} - k^{2}_{y} \right) \
\mathcal{F}
\left(
\mathcal{F}^{-1}
diff --git a/Cat_UG_00/ref.bib b/Cat_UG_00/ref.bib
index 70185125b8b52045eff83b04b67552699d99f27d..76438b226f19a8e0c9d24c4bfa328debe57925b9 100644
--- a/Cat_UG_00/ref.bib
+++ b/Cat_UG_00/ref.bib
@@ -65,6 +65,14 @@
@string{ pss = {\it Planet.\ Space Sci.}}
%==========================================================================
+@article{arakawa1966,
+ author = {A. Arakawa},
+ title = {{C}omputational {D}esign for {L}ong-{T}erm {N}umerical {I}ntegration of the {E}quations of {F}luid {M}otion: {T}wo-{D}imensional {I}ncompressible {F}low. {P}art {I}},
+ journal = {J. Comput. Phys.},
+ pages = {119--143 he},
+ year = {1966},
+ volume = {1}
+}
@book{batchelor1967,
author = {G. K. Batchelor},
@@ -160,3 +168,20 @@
pages = {253--259}
}
+@article{salmonandtalley1989,
+ author = {R. Salmon and D. Talley},
+ title = {Generalizations of Arakawa's Jacobian},
+ journal = {\it Journal of Computational Physics},
+ year = {1989},
+ volume = {83}
+ pages = {247--259}
+}
+
+@article{tungandorlando2003,
+ author = {K. K. Tung and W. W. Orlando},
+ title = {{O}n the Differences between 2D and QG Turbulence},
+ journal = {\it Discrete and Continuous Dynamical Systems-Series B},
+ year = {2003},
+ volume = {3},
+ pages = {145--162}
+}
diff --git a/cat/dat/GUI.cfg b/cat/dat/GUI.cfg
index 35d79c153b76bf83588635acfc5b5f31a8cdfbfb..91adfa92779aa18b2356f3b778ee44edc0757e21 100644
--- a/cat/dat/GUI.cfg
+++ b/cat/dat/GUI.cfg
@@ -9,21 +9,21 @@ Array:GQ
Plot:ISOREC
Palette:AUTO
Title:Vorticity
-Geometry: 1000 1000 1 0
+Geometry: 1000 1000 1 1
[Window 01]
-Array:GXM
-Plot:LINE
+Array:C4
+Plot:ISOAMP
Palette:AUTO
-Title:GXM
-Geometry: 853 367 853 -1
+Title:Vorticity
+Geometry: 540 1000 1050 1
[Window 02]
Array:QC
Plot:ISOAMP
Palette:AMPLI
Title:C4
-Geometry: 853 367 1706 -1
+Inactive: 853 367 1706 -1
[Window 03]
Array:GP
diff --git a/cat/dat/GUI_Amp.cfg b/cat/dat/GUI_Amp.cfg
new file mode 100644
index 0000000000000000000000000000000000000000..91adfa92779aa18b2356f3b778ee44edc0757e21
--- /dev/null
+++ b/cat/dat/GUI_Amp.cfg
@@ -0,0 +1,139 @@
+Hamburg GUI Config File Version 16
+Screen: 2560x1418
+
+WinRows = 3
+WinCols = 3
+
+[Window 00]
+Array:GQ
+Plot:ISOREC
+Palette:AUTO
+Title:Vorticity
+Geometry: 1000 1000 1 1
+
+[Window 01]
+Array:C4
+Plot:ISOAMP
+Palette:AUTO
+Title:Vorticity
+Geometry: 540 1000 1050 1
+
+[Window 02]
+Array:QC
+Plot:ISOAMP
+Palette:AMPLI
+Title:C4
+Inactive: 853 367 1706 -1
+
+[Window 03]
+Array:GP
+Plot:MAPHOR
+Projection:POLAR
+Rotation factor:0
+Palette:P
+Title:Surface Pressure [hPa]
+Inactive: 853 367 0 389
+
+[Window 04]
+Array:GU
+Plot:MAPTRA
+Projection:AZIMUTHAL
+Rotation factor:0
+Palette:U
+Title:Tracer Level 3
+Inactive: 853 367 853 389
+
+[Window 05]
+Array:GV
+Plot:ISOLON
+Palette:U
+Title:Meridional Wind [m/s] Latitude 42N
+Inactive: 853 367 1706 389
+
+[Window 06]
+Array:GP
+Plot:ISOHOV
+Palette:P
+Title:Ps Hovmoeller Latitude 42N
+Inactive: 853 367 0 779
+
+[Window 07]
+Array:SCALAR
+Plot:ISOTS
+Palette:AUTO
+Title:Timeseries
+Inactive: 853 367 853 779
+
+[Window 08]
+Array:SCALAR
+Plot:ISOTAB
+Palette:AUTO
+Title:Tables
+Inactive: 853 367 1706 779
+
+[Control Window]
+Geometry: 920 122 820 1171
+
+# Scalar attributes for timeseries and table window
+
+[Scalar 00]
+Name:T
+Sub:
+Unit:C
+Scale:
+
+[Scalar 01]
+Name:RMS Div
+Sub:
+Unit:1/s
+Scale:-6
+
+[Scalar 02]
+Name:PE+KE
+Sub:
+Unit:m2/s2
+Scale:
+
+[Scalar 03]
+Name:RMS Ps
+Sub:
+Unit:hPa
+Scale:
+
+[Scalar 04]
+Name:Vort
+Sub:
+Unit:1/s
+Scale:
+
+# Parameter attributes for change menu
+
+[Parameter 00]
+ParName:NGUI
+ParInc: 1.0000
+ParMin: 1.0000
+ParMax: 1000.0000
+
+[Parameter 01]
+ParName:QMAX
+ParInc: 1.0000
+ParMin: 0.0000
+ParMax: 1000.0000
+
+[Parameter 02]
+ParName:DTNS
+ParInc: 5.0000
+ParMin: -95.0000
+ParMax: 100.0000
+
+[Parameter 03]
+ParName:NSYNC
+ParInc: 1.0000
+ParMin: 0.0000
+ParMax: 1.0000
+
+[Parameter 04]
+ParName:EPSYNC
+ParInc: 1.0000
+ParMin: 0.0000
+ParMax: 100.0000
diff --git a/cat/src/cat.f90 b/cat/src/cat.f90
index 2a262e08a74a3b7dd5d642f67fa727f1312698a8..a429db51b775cf006f7dfc3723be81ef6b3f0be6 100644
--- a/cat/src/cat.f90
+++ b/cat/src/cat.f90
@@ -5,14 +5,14 @@ module catmod
! *********************************************
! * *
-! * CAT *
+! * CAT *
! * *
! * Computer Aided Turbulence *
! * *
! * Version 1.1 July 2016 *
! * *
! *********************************************
-! * Theoretical Meteorology - KlimaCampus *
+! * Theoretical Meteorology - KlimaCampus *
! * University of Hamburg *
! *********************************************
! * Hartmut Borth - Edilbert Kirk *
@@ -42,13 +42,13 @@ module catmod
character (256) :: catversion = "July 2016, Version 0.1"
integer :: nshutdown = 0 ! Flag to stop program
-logical :: lrsttest = .false. ! flag set to .true. for restart test,
- ! parameter nsteps is not written
+logical :: lrsttest = .false. ! flag set to .true. for restart test,
+ ! parameter nsteps is not written
! to restart file. lrsttest is set to
! true if a file RSTTEST is found in the
! run directory. Call <make rsttest> to
! do the restart test. To clean the run after
- ! a restart test call <make cleanresttest>
+ ! a restart test call <make cleanresttest>
! ***************************
@@ -109,20 +109,20 @@ integer, parameter :: ningp = 5
integer, parameter :: ninsp = 5
integer :: ingp(ningp) = &
(/ qcde , &
- qfrccde , &
- 0 , &
- 0 , &
- 0 &
- /)
+ qfrccde , &
+ 0 , &
+ 0 , &
+ 0 &
+ /)
integer :: insp(ninsp) = &
(/ qcde , &
qfrccde , &
- 0 , &
- 0 , &
+ 0 , &
+ 0 , &
0 &
- /)
+ /)
-!--- codes of variables to be written to cat_gp or cat_sp
+!--- codes of variables to be written to cat_gp or cat_sp
integer, parameter :: noutgp = 5
integer, parameter :: noutsp = 5
integer :: outgp(noutgp) = &
@@ -142,7 +142,7 @@ integer :: outsp(noutsp) = &
! *******************************
-! * Basic diagnostic parameters *
+! * Basic diagnostic parameters *
! *******************************
integer :: tsps ! time steps per second (cpu-time)
@@ -164,7 +164,7 @@ real(8) :: ly = twopi ! in y-direction (scale L_x = X/2pi)
real(8) :: alpha = 0.0 ! alpha = 1/R_hat**2 [1/m**2]
! with the non-dimensional Rossby
! radius Ro_hat = Ro/L_x
-
+
real(8) :: beta = 0.0 ! ambient vorticity gradient [1/m*s]
!---------------------!
@@ -176,20 +176,20 @@ integer :: diss_mthd = 1 ! dissipation method
! sig and lam and the powers psig and
! plam
! 2: Laplacian viscosity and friction
- ! characterized by the reciprocal
+ ! characterized by the reciprocal
! damping time-scales rtsig and rtlam,
! the cut-off wave-numbers ksig and klam
- ! and the powers psig and plam
-
+ ! and the powers psig and plam
+
!----------------------------------!
! Laplacian viscosity and friction !
!----------------------------------!
-integer, parameter :: nsig = 2 ! maximum number of terms of Laplacian
+integer, parameter :: nsig = 2 ! maximum number of terms of Laplacian
! dissipation on small scales
-
-integer, parameter :: nlam = 2 ! maximum number of terms of Laplacian
+
+integer, parameter :: nlam = 2 ! maximum number of terms of Laplacian
! dissipation on large scales
!--- definition of dissipation on small scales
@@ -199,11 +199,11 @@ real(8) :: psig (nsig) = & ! powers of Laplacian parameterizing
/)
real(8) :: sig(nsig) = & ! coefficients of different powers
(/ 9.765625d-05, & ! of the Laplacian [m^2*psig/s]
- 9.094947d-11 &
+ 9.094947d-11 &
/)
real(8) :: rtsig(nsig) = & ! 1/time-scale of different powers
(/ 1.d-1, & ! of the Laplacian [1/s]
- 1.d+2 &
+ 1.d+2 &
/)
integer :: ksig (nsig) = & ! lower "cut-off" wave number of different
(/ 320, & ! powers of Laplacian
@@ -214,14 +214,14 @@ integer :: ksig (nsig) = & ! lower "cut-off" wave number of different
real(8) :: plam (nlam) = & ! powers of Laplacian modelling viscosity
(/ -1.d0, & ! on large scales plam <= 0
-4.d0 &
- /)
+ /)
real(8) :: lam(nlam) = & ! coefficients of different powers
(/ 0.d0, & ! of the Laplacian [m^(-2*psig)/s]
- 0.d0 &
+ 0.d0 &
/)
real(8) :: rtlam(nlam) = & ! 1/time-scale of different powers
(/ 0.d0, & ! of the Laplacian [1/s]
- 0.d0 &
+ 0.d0 &
/)
integer :: klam (nlam) = & ! lower "cut-off" wave number of different
(/ 1, & ! powers of Laplacian
@@ -243,16 +243,16 @@ integer :: npert = 0 ! initial perturbation switch
! 2 = white noise symmetric perturbation about the axis
! y = pi (zero mean vorticity in the upper and
! lower part of the fluid domain separately)
- ! 3 = white noise anti-symmetricy perturbation about
- ! the axis y = pi (zero mean vorticity in the upper
+ ! 3 = white noise anti-symmetricy perturbation about
+ ! the axis y = pi (zero mean vorticity in the upper
! and lower power separately)
! 4 = white noise symmetric perturbation about the axis
! x = pi (zero mean vorticity in the upper and
! lower part of the fluid domain separately)
- ! 5 = white noise anti-symmetricy perturbation about
- ! the axis x = pi (zero mean vorticity in the upper
+ ! 5 = white noise anti-symmetricy perturbation about
+ ! the axis x = pi (zero mean vorticity in the upper
! and lower power separately)
-
+
real(8) :: apert = 1.0d-5 ! amplitude of perturbation
@@ -311,11 +311,11 @@ integer :: jacmthd = 1 ! approximation method of Jacobian
! 0 : no Jacobian
! 1 : divergence form (uq)_x + (vq)_y
! 2 : advection form uq_x + vq_y
- ! 3 : invariant form
+ ! 3 : invariant form
!--- time integration
integer :: nsteps = 10000 ! number of time steps to be integrated
-integer :: tstep = 0 ! current time step (since start of runs)
+integer :: tstep = 0 ! current time step (since start of runs)
integer :: tstop = 0 ! last time step of run
integer :: tstp_mthd = 1 ! time stepping method
@@ -326,18 +326,18 @@ integer :: nstdout = 2500 ! time steps between messages to
integer :: ndiag = 500 ! time steps between test outputs into
- ! out_diag (-1 no test outputs)
+ ! out_diag (-1 no test outputs)
integer :: ngp = 100 ! time steps between output of grid point
! fields (-1 = no output)
integer :: nsp = 100 ! time steps between output of spectral
! fields (-1 = no output)
-integer :: ncfl = 100 ! time steps between cfl-check
+integer :: ncfl = 100 ! time steps between cfl-check
! (-1 no cfl check)
integer :: ntseri = 100 ! time steps between time-series output
! (-1 no time-series)
-
+
real(8) :: dt = 1.d-3 ! length of time step [s]
!--------------------------------------------!
@@ -358,7 +358,7 @@ real(8), allocatable :: guq(:,:) ! u*q [m/s^2]
real(8), allocatable :: gvq(:,:) ! v*q [m/s^2]
!--- case 2 (!! variables contain different fields depending on context)
-real(8), allocatable :: gqx (:,:) ! dq/dx [1/ms]
+real(8), allocatable :: gqx (:,:) ! dq/dx [1/ms]
real(8), allocatable :: gqy (:,:) ! dq/dy [1/ms]
real(8), allocatable :: gjac(:,:) ! jacobian [s^-2]
@@ -372,7 +372,7 @@ real(4), allocatable :: ggui(:,:) ! single precision transfer
!----------------------------------------------------------!
! variables in spectral space, representation as imaginary !
-! and real part (prefix f) used for fourier transformation !
+! and real part (prefix f) used for fourier transformation !
! and complex representation (prefix c) used for time !
! evolution !
!----------------------------------------------------------!
@@ -424,10 +424,10 @@ complex(8), allocatable :: cli(:,:) ! linear time propagation
! *******************
!--- gui communication (guimod)
-integer :: ngui = 1 ! global switch and parameter
- ! ngui > 0 GUI = on
- ! ngui specifies moreover the number of
- ! time-steps between two calls of gui_transfer
+integer :: ngui = 1 ! global switch and parameter
+ ! ngui > 0 GUI = on
+ ! ngui specifies moreover the number of
+ ! time-steps between two calls of gui_transfer
! which exchanges data between GUI and CAT
integer :: nguidbg = 0 ! GUI debug mode
@@ -437,9 +437,9 @@ real(4) :: parc(5) = 0.0 ! timeseries display
!--- code of predefined simulations (simmod)
-integer :: nsim = 0 ! 0 no predefined simulation is specified
+integer :: nsim = 0 ! 0 no predefined simulation is specified
! nsim > 0 predefined simulation is run
- !
+ !
! available predefined simulations (experiments):
! -----------------------------------------------
! code name
@@ -447,19 +447,19 @@ integer :: nsim = 0 ! 0 no predefined simulation is specified
! 1 decaying_jet01
! 51 top-hat wind-forcing
! 52 top-hat wind-forcing
- ! -----------------------------------------------
- !
+ ! -----------------------------------------------
+ !
! Predefined simulations are given in the dat
- ! directory as sim_XXXX.nl with XXXX the code
+ ! directory as sim_XXXX.nl with XXXX the code
! To activate a given simulation one has to copy
- ! a given sim_XXXX.nl to sim_namelist in the run
+ ! a given sim_XXXX.nl to sim_namelist in the run
! directory.
- ! -----------------------------------------------
+ ! -----------------------------------------------
!--- usermod (usermod)
integer :: nuser = 0 ! 1/0 user mode is switched on/off.
- ! In user mode it is possible to introduce
- ! new code into CAT (see chapter <Modifying
+ ! In user mode it is possible to introduce
+ ! new code into CAT (see chapter <Modifying
! CAT> in the User's Guide).
@@ -480,10 +480,10 @@ real(8), allocatable :: guym(:) ! mean x-velocity allong y-dir [m/s]
real(8), allocatable :: gvxm(:) ! mean y-velocity allong x-dir [m/s]
real(8), allocatable :: gvym(:) ! mean y-velocity allong y-dir [m/s]
-real(4), allocatable :: gguixm(:) ! single precision mean in x-dir for gui
-real(4), allocatable :: gguiym(:) ! single precision mean in y-dir for gui
+real(4), allocatable :: gguixm(:) ! single precision mean in x-dir for gui
+real(4), allocatable :: gguiym(:) ! single precision mean in y-dir for gui
-real(4), allocatable :: ggxm(:,:) ! single precision mean in y-dir for gui
+real(4), allocatable :: ggxm(:,:) ! single precision mean in y-dir for gui
end module catmod
@@ -684,7 +684,7 @@ if (lcatnl) then
read(nucatnl,cat_nl)
endif
-!--- check consistency of namelist parameters
+!--- check consistency of namelist parameters
if (jacmthd .lt. 0 .or. jacmthd .gt. 3) then
write(nudiag, &
'(/," ************************************************")')
@@ -790,21 +790,21 @@ allocate(gpsi(1:ngx,1:ngy)) ; gpsi(:,:) = 0.0 ! stream function
allocate(ggui(1:ngx,1:ngy)) ; ggui(:,:) = 0.0 ! GUI transfer
-!--- spetral space
-allocate(fu(0:nfx,0:nfy)) ; fu(:,:) = 0.0 ! u
-allocate(fv(0:nfx,0:nfy)) ; fv(:,:) = 0.0 ! v
+!--- spetral space
+allocate(fu(0:nfx,0:nfy)) ; fu(:,:) = 0.0 ! u
+allocate(fv(0:nfx,0:nfy)) ; fv(:,:) = 0.0 ! v
allocate(k2(0:nkx,0:nfy)) ; k2(:,:) = 0.0 ! Laplacian
allocate(k2pa(0:nkx,0:nfy)) ; k2pa(:,:) = 0.0 ! modified Laplacian
allocate(rk2pa(0:nkx,0:nfy)) ; rk2pa(:,:) = 0.0 ! modified Laplacian^-1
allocate(kxrk2pa(0:nkx,0:nfy)) ; kxrk2pa(:,:) = 0.0 ! q --> v
allocate(kyrk2pa(0:nkx,0:nfy)) ; kyrk2pa(:,:) = 0.0 ! q --> u
-allocate(kx2mky2(0:nkx,0:nfy)) ; kx2mky2(:,:) = 0.0 ! utility for Jacobian 3
-allocate(kxky (0:nkx,0:nfy)) ; kxky (:,:) = 0.0 ! utility for Jacobian 3
+allocate(kx2mky2(0:nkx,0:nfy)) ; kx2mky2(:,:) = 0.0 ! utility for Jacobian 3
+allocate(kxky (0:nkx,0:nfy)) ; kxky (:,:) = 0.0 ! utility for Jacobian 3
-allocate(cli(0:nkx,0:nfy)) ; cli(:,:) = (0.0,0.0) ! linear time propagator
+allocate(cli(0:nkx,0:nfy)) ; cli(:,:) = (0.0,0.0) ! linear time propagator
allocate(cq(0:nkx,0:nfy)) ; cq(:,:) = (0.0,0.0) ! vorticity
allocate(c4(0:nkx,0:nfy)) ; c4(:,:) = (0.0,0.0) ! vorticity
@@ -838,7 +838,7 @@ case(1)
allocate(guq(1:ngx,1:ngy)) ; guq(:,:) = 0.0 ! u*q
allocate(gvq(1:ngx,1:ngy)) ; gvq(:,:) = 0.0 ! v*q
- !--- spectral fields
+ !--- spectral fields
allocate(fuq(0:nfx,0:nfy)) ; fuq(:,:) = 0.0 ! u*q
allocate(fvq(0:nfx,0:nfy)) ; fvq(:,:) = 0.0 ! v*q
case(2)
@@ -849,15 +849,15 @@ case(2)
allocate(gqy(1:ngx,1:ngy)) ; gqy(:,:) = 0.0 ! qy
allocate(gjac(1:ngx,1:ngy)) ; gjac(:,:) = 0.0 ! jacobian in grid-space
- !--- spectral fields
+ !--- spectral fields
allocate(fqx(0:nfx,0:nfy)) ; fqx(:,:) = 0.0 ! u*qx or qx
allocate(fqy(0:nfx,0:nfy)) ; fqy(:,:) = 0.0 ! v*qy or qy
case(3)
!--- allocate fields used by jacobian
- !--- grid point fields
- allocate(gv2mu2(1:ngx,1:ngy)) ; gv2mu2(:,:) = 0.0 ! v^2-u^2
- allocate(guv (1:ngx,1:ngy)) ; guv (:,:) = 0.0 ! u*v
- !--- spetral fields
+ !--- grid point fields
+ allocate(gv2mu2(1:ngx,1:ngy)) ; gv2mu2(:,:) = 0.0 ! v^2-u^2
+ allocate(guv (1:ngx,1:ngy)) ; guv (:,:) = 0.0 ! u*v
+ !--- spetral fields
allocate(fv2mu2(0:nfx,0:nfy)) ; fv2mu2(:,:) = 0.0 ! v^2-u^2
allocate(fuv (0:nfx,0:nfy)) ; fuv (:,:) = 0.0 ! u*v
print *, "init_jacobian case 3"
@@ -879,34 +879,34 @@ select case (jacmthd)
case (1)
!--- deallocate fields used by jacobian
- !--- grid point fields
+ !--- grid point fields
deallocate(guq)
deallocate(gvq)
- !--- spetral fields
+ !--- spetral fields
deallocate(fuq)
deallocate(fvq)
case (2)
!--- deallocate fields used by jacobian
- !--- grid point fields
+ !--- grid point fields
deallocate(gqx)
deallocate(gqy)
deallocate(gjac)
- !--- spetral fields
+ !--- spetral fields
deallocate(fqx)
deallocate(fqy)
case (3)
!--- deallocate fields used by jacobian
- !--- grid point fields
+ !--- grid point fields
deallocate(gv2mu2)
deallocate(guv)
- !--- spetral fields
+ !--- spetral fields
deallocate(fv2mu2)
deallocate(fuv)
@@ -1162,7 +1162,7 @@ integer :: jx,jy,n
!
! arg = -dt*[diss_sig + diss_lam + beta_term]
!
-! with
+! with
! diss_sig = -sum_j=1,nsig sig(j)*k^(2*psig(j))
! diss_lam = -sum_j=1,nlam lam(j)*k^(2*plam(j))
! b_term = i*beta*kx/(k^2 + alpha)
@@ -1230,7 +1230,7 @@ integer :: jx,jy
if (nforc .eq. 0) return
-!---
+!---
ent=0.d0
do jy = 0, nfy
do jx = 0, nkx
@@ -1239,10 +1239,10 @@ do jy = 0, nfy
if (jy.ne.0.or.jx.ne.0) then
if (sqrt(k2tmp).ge.kfmin.and.sqrt(k2tmp).le.kfmax) then
nk = nk + 1
- in(nk,1) = jx
+ in(nk,1) = jx
in(nk,2) = jy
! ent=ent+k2+alpha
- ent=ent+k2pa(jy,jx)
+ ent=ent+k2pa(jx,jy)
endif
endif
enddo
@@ -1281,7 +1281,7 @@ if (nforc .eq. 0) return
!--- forcing is specified by input files
-!--- examples are produced in simmod.f90
+!--- examples are produced in simmod.f90
!--- produce masks
@@ -1328,7 +1328,7 @@ select case(npert)
do jy = 1,ngy/2
call random_number(xtmp)
xtmp = 2.0*apert*(xtmp - sum(xtmp)*rnx)
- gqpert(:,jy) = xtmp(:)
+ gqpert(:,jy) = xtmp(:)
gqpert(:,ngy+1-jy) = xtmp(:)
enddo
call grid_to_fourier(gqpert,cqpert,nfx,nfy,ngx,ngy)
@@ -1339,35 +1339,35 @@ select case(npert)
do jy = 1,ngy/2
call random_number(xtmp)
xtmp = 2.0*apert*(xtmp - sum(xtmp)*rnx)
- gqpert(:,jy) = xtmp(:)
+ gqpert(:,jy) = xtmp(:)
gqpert(:,ngy+1-jy) = -xtmp(:)
enddo
call grid_to_fourier(gqpert,cqpert,nfx,nfy,ngx,ngy)
cqpert(0,0) = (0.0,0.0)
cq = cq + cqpert
case(4)
- !--- symmetric about x = pi
+ !--- symmetric about x = pi
do jx = 1,ngx/2
call random_number(ytmp)
ytmp = 2.0*apert*(ytmp - sum(ytmp)*rny)
- gqpert(jx,:) = ytmp(:)
+ gqpert(jx,:) = ytmp(:)
gqpert(ngx+1-jx,:) = ytmp(:)
enddo
call grid_to_fourier(gqpert,cqpert,nfx,nfy,ngx,ngy)
cqpert(0,0) = (0.0,0.0)
cq = cq + cqpert
case(5)
- !--- anti-symmetric about x = pi
+ !--- anti-symmetric about x = pi
! do jx = 1,ngx/2
! call random_number(ytmp)
! ytmp = 2.0*apert*(ytmp - sum(ytmp)*rny)
-! gqpert(jx,:) = ytmp(:)
+! gqpert(jx,:) = ytmp(:)
! gqpert(ngx+1-jx,:) = -ytmp(:)
! enddo
do jy = 1,ngy/2
call random_number(xtmp)
xtmp = 2.0*apert*(xtmp - sum(xtmp)*rnx)
- gqpert(:,jy) = xtmp(:)
+ gqpert(:,jy) = xtmp(:)
gqpert(:,ngy+1-jy) = -xtmp(:)
enddo
gqpert = transpose(gqpert)
@@ -1448,7 +1448,7 @@ if((ngp .gt. 0) .and. mod(tstep,ngp).eq.0) then
case (qcde)
call cat_wrtgp(nugp,gq,qcde,0)
end select
- enddo
+ enddo
endif
if((nsp .gt. 0) .and. mod(tstep,nsp).eq.0) then
@@ -1480,13 +1480,18 @@ implicit none
ggui(:,:) = gq(:,:) ! double precision -> single
call guiput("GQ" // char(0), ggui, ngx, ngy, 1)
+! double -> single and center about ky = 0
+c4(:,0:nky-1) = cq(:,nky+1:nfy)
+c4(:,nky:nfy) = cq(:,0:nky)
+call guiput("C4" // char(0), c4, nkx+1, nfy+1, 2) ! fc
+
if (npost > 0) then
!--- zonal means
gguixm(:) = gqxm(:) ! double -> single
- call guiput("GQXM" // char(0), gguixm, ngy, 1, 1) ! q
+ call guiput("GQXM" // char(0), gguixm, ngy, 1, 1) ! q
gguixm(:) = gpsixm(:) ! double -> single
- call guiput("GPSIXM" // char(0), gguixm, ngy, 1, 1) ! psi
+ call guiput("GPSIXM" // char(0), gguixm, ngy, 1, 1) ! psi
! gguixm(:) = guxm(:) ! double -> single
! call guiput("GUXM" // char(0), gguixm, ngy, 1, 1) ! u
@@ -1502,10 +1507,10 @@ if (npost > 0) then
!--- meridional means
gguiym(:) = gqym(:) ! double -> single
- call guiput("GQYM" // char(0), gguiym, ngx, 1, 1) ! q
+ call guiput("GQYM" // char(0), gguiym, ngx, 1, 1) ! q
gguiym(:) = gpsiym(:) ! double -> single
- call guiput("GPSIYM" // char(0), gguiym, ngx, 1, 1) ! psi
+ call guiput("GPSIYM" // char(0), gguiym, ngx, 1, 1) ! psi
gguiym(:) = guym(:) ! double -> single
call guiput("GUYM" // char(0), gguiym, ngx, 1, 1) ! u
@@ -1513,9 +1518,6 @@ if (npost > 0) then
gguiym(:) = gvym(:) ! double -> single
call guiput("GVYM" // char(0), gguiym, 1, ngx, 1) ! v
- c4(:,:) = cq(:,:)
- call guiput("C4" // char(0), c4, nkx+1, nfy+1, 2) ! v
-
endif
return
@@ -1603,16 +1605,16 @@ subroutine init_tstep
use catmod
implicit none
-real(8) :: dt2
+real(8) :: dt2
dt2 = dt/2
!--- determine tstop and return if tstep > 0
if (tstep .eq. 0) then
- tstop = tstep + nsteps
+ tstop = tstep + nsteps
else
- tstop = tstep - 1 + nsteps
+ tstop = tstep - 1 + nsteps
return
endif
@@ -1671,10 +1673,10 @@ allocate(guym(1:ngx)) ; guym(:) = 0.0 ! u-mean in y-dir [m/s]
allocate(gvxm(1:ngy)) ; gvxm(:) = 0.0 ! v-mean in x-dir [m/s]
allocate(gvym(1:ngx)) ; gvym(:) = 0.0 ! v-mean in y-dir [m/s]
-allocate(gguixm(1:ngy)) ; gguixm(:) = 0.0 ! single precision mean in x-dir
-allocate(gguiym(1:ngx)) ; gguiym(:) = 0.0 ! single precision mean in y-dir
+allocate(gguixm(1:ngy)) ; gguixm(:) = 0.0 ! single precision mean in x-dir
+allocate(gguiym(1:ngx)) ; gguiym(:) = 0.0 ! single precision mean in y-dir
-allocate(ggxm(1:ngx,4)) ; ggxm(:,:) = 0.0 ! single precision mean in x-dir
+allocate(ggxm(1:ngx,4)) ; ggxm(:,:) = 0.0 ! single precision mean in x-dir
return
end subroutine init_post
@@ -1688,11 +1690,11 @@ use catmod
implicit none
if (npost > 0) then
- deallocate(gqxm)
- deallocate(gqym)
+ deallocate(gqxm)
+ deallocate(gqym)
deallocate(gpsixm)
- deallocate(gpsiym)
+ deallocate(gpsiym)
deallocate(guxm)
deallocate(guym)
@@ -1860,7 +1862,7 @@ call put_restart_iarray('npert',npert,1,1)
call put_restart_array ('apert',apert,1,1)
call put_restart_iarray('nforc',nforc,1,1)
call put_restart_iarray('kfmin',kfmin,1,1)
-call put_restart_iarray('kfmax',kfmax,1,1)
+call put_restart_iarray('kfmax',kfmax,1,1)
call put_restart_array ('aforc',aforc,1,1)
call put_restart_array ('tforc',tforc,1,1)
call put_restart_iarray('myseed',myseed,mxseedlen,1)
@@ -1894,7 +1896,7 @@ subroutine close_files
use catmod
if (lrst) close(nurstini)
-if (lcatnl) close(nucatnl)
+if (lcatnl) close(nucatnl)
close(nurstfin)
close(nudiag)
if (ntseri .gt. 0) close(nutseri)
@@ -1930,7 +1932,7 @@ case (1)
!--- (!!! Jacobian has different sign than in CAT-UG !!!)
do jx = 0, nkx
- cjac0(jx,:) = &
+ cjac0(jx,:) = &
cmplx( kx(jx)*fuq(jx+jx+1,:)+ky(:)*fvq(jx+jx+1,:), &
-kx(jx)*fuq(jx+jx ,:)-ky(:)*fvq(jx+jx ,:))
enddo
@@ -1943,18 +1945,18 @@ case (2)
case (3)
!--- Jacobian in invariant form (third representation in CAT-UG)
- gv2mu2 = gv**2 - gu**2
+ gv2mu2 = gv**2 - gu**2
guv = gu*gv
call grid_to_fourier(gv2mu2,fv2mu2,nfx,nfy,ngx,ngy)
call grid_to_fourier(guv,fuv,nfx,nfy,ngx,ngy)
do jx = 0, nkx
- cjac0(jx,:) = &
+ cjac0(jx,:) = &
cmplx(kxky(jx,:)*fv2mu2(2*jx ,:) + kx2mky2(jx,:)*fuv(2*jx ,:), &
kxky(jx,:)*fv2mu2(2*jx+1,:) + kx2mky2(jx,:)*fuv(2*jx+1,:))
enddo
-
+
end select
if (jac_scale .ne. 1.0 .or. jac_scale .ne. 0.0) &
@@ -2021,9 +2023,9 @@ eni=0.d0
enf=0.d0
select case (nforc)
- case (1)
+ case (1)
cq = cq + cqfrc
-
+
case (2)
do ifk = 1,nk
i = in(ifk,1)
@@ -2126,7 +2128,7 @@ real(8) :: cfl
real(8) :: maxu,maxv
-!--- check courant number
+!--- check courant number
maxu = maxval(abs(gu(:,:))) * dt * ngx / lx
maxv = maxval(abs(gv(:,:))) * dt * ngy / ly
@@ -2145,10 +2147,10 @@ subroutine init_ops
use catmod
implicit none
-integer :: jx,jy
-
+integer :: jx,jy
+
kx2 = kx*kx
-kx2(0) = 1.0
+kx2(0) = 1.0
ky2 = ky*ky
@@ -2157,7 +2159,7 @@ do jy = 0, nfy
k2 (jx,jy) = (kx2(jx)+ky2(jy)) ! - Laplacian psi --> -q
k2pa (jx,jy) = (kx2(jx)+ky2(jy))+alpha ! - mod Laplacian psi --> -q
rk2pa (jx,jy) = 1.0d0/(k2(jx,jy)+alpha) ! 1/mod Laplacian q --> -psi
- kxrk2pa(jx,jy) = kx(jx)*rk2pa(jx,jy) ! q ---> v/i
+ kxrk2pa(jx,jy) = kx(jx)*rk2pa(jx,jy) ! q ---> v/i
kyrk2pa(jx,jy) = ky(jy)*rk2pa(jx,jy) ! q ---> u/i
kx2mky2(jx,jy) = kx2(jx)-ky2(jy) ! utility Jacobian 3
kxky (jx,jy) = kx(jx)*ky(jy) ! utility Jacobian 3
diff --git a/cat/src/guix11.c b/cat/src/guix11.c
index e2e33a5b5f60135126d17efad57c20302002032f..7f0de9d1497ed2c6bf7913f5220f34689eb4fd9b 100644
--- a/cat/src/guix11.c
+++ b/cat/src/guix11.c
@@ -1,5 +1,5 @@
/*
- guix11 - a GUI for PUMA, PLASIM & CAT
+ guix11 - a GUI for PUMA, PLASIM & CAT
2016 Edilbert Kirk & Hartmut Borth
This program is free software; you can redistribute it and/or modify
@@ -925,7 +925,7 @@ void AzimuthalImage(struct MapImageStruct *s, struct MapImageStruct *d)
int dy ; // centre relative y position
int p00; // euqator
int l00; // reference longitude
-
+
unsigned int dih; // destination image height
unsigned int diw; // destination image width
unsigned int dpw; // destination image padded width
@@ -1008,15 +1008,15 @@ void SwapIEEE16(char W[2])
{
char B;
- B = W[0]; W[0] = W[1]; W[1] = B;
+ B = W[0]; W[0] = W[1]; W[1] = B;
}
void SwapIEEE32(char W[4])
{
char B;
- B = W[0]; W[0] = W[3]; W[3] = B;
- B = W[1]; W[1] = W[2]; W[2] = B;
+ B = W[0]; W[0] = W[3]; W[3] = B;
+ B = W[1]; W[1] = W[2]; W[2] = B;
}
int ReadINT(FILE *fpi)
@@ -1102,8 +1102,8 @@ void ReadImage(struct MapImageStruct *ei, char *filename)
BuffImageData = malloc(PicBytes);
fseek(fp,OffBits,SEEK_SET);
n = fread(BuffImageData,PicBytes,1,fp);
- fclose(fp);
-
+ fclose(fp);
+
ei->X = XCreateImage(display,CopyFromParent,ScreenD,ZPixmap,0,
ei->d,PadWidth,ImageBMI.Height,8,0);
@@ -1252,7 +1252,7 @@ int AllocateColorCells(struct ColorStrip cs[])
XAllocNamedColor(display,colormap,cs[i].Name,&xcolor1,&xcolor2);
cs[i].pixel = xcolor1.pixel;
++i;
- }
+ }
return i;
}
@@ -1373,13 +1373,13 @@ void TestWindow(int xx, int yy, int wi, int he, int *x, int *y,
unsigned int DepthReturn = 0;
unsigned int BorderReturn = 0;
Window TW,Parent,Child;
-
+
TW = XCreateWindow(display,RootWindow(display,screen_num),
xx,yy,wi,he, // x,y,w,h
0,CopyFromParent,InputOutput, // border, depth, class
CopyFromParent,0,NULL); // visual, valuemask, attributes
XSelectInput(display,TW,ExposureMask);
- XMapWindow(display,TW);
+ XMapWindow(display,TW);
XMoveWindow(display,TW,xx,yy);
XNextEvent(display,&CowEvent); // Wait until WM mapped it
XGetGeometry(display,TW,&Parent,x,y,W,H,&BorderReturn,&DepthReturn);
@@ -1398,7 +1398,7 @@ void CreateTestWindow(void)
{
int X,Y,xp,yp;
unsigned int W,H;
-
+
// Open a test window with displacement x = 100 and y = 100
// Test the returned coordinates for upper left corner
// and compute left margin (border) and top margin (title bar)
@@ -1606,7 +1606,7 @@ void CreateControlWindow(void)
strcpy(Title1,"Unknown model");
if (Model == 0) // PUMA
{
- if (MRpid < 0)
+ if (MRpid < 0)
strcpy(Title1,"PUMA - KlimaCampus Hamburg");
else
sprintf(Title1,"Run %d: PUMA - KlimaCampus Hamburg",MRpid);
@@ -1836,7 +1836,7 @@ void ShowGridStatus(void)
if (Grid) CheckMark(x,y,d);
}
-
+
int RedrawControlWindow(void)
{
char Text[80];
@@ -1847,7 +1847,7 @@ int RedrawControlWindow(void)
status = XGetWindowAttributes(display,Cow,&CurAtt);
WinXSize = CurAtt.width;
WinYSize = CurAtt.height;
-
+
XSetForeground(display,gc,BlackPix);
XSetBackground(display,gc,WhitePix);
@@ -1865,7 +1865,7 @@ int RedrawControlWindow(void)
for (i=0 ; i < PSDIM ; ++i)
if (pixelstar[j][i] == '*')
XDrawPoint(display,Cow,gc,i+x1,j+y1);
-
+
XSetForeground(display,gc,LightRed.pixel);
x1 = 10; x2 = 40 ; y1 = OffsetY + 10 ; y2 = OffsetY + 40;
XDrawLine(display,Cow,gc,x2 ,y1-1,x2 ,y2 );
@@ -1895,7 +1895,7 @@ int RedrawControlWindow(void)
XSetForeground(display,gc,Blue.pixel);
XFillPolygon(display,Cow,gc,PauseButton1,4,Convex,CoordModeOrigin);
XFillPolygon(display,Cow,gc,PauseButton2,4,Convex,CoordModeOrigin);
-
+
x1 = 95; x2 = 102; y1 = OffsetY + 10; y2 = OffsetY + 40;
XSetForeground(display,gc,DarkBlue.pixel);
XDrawLine(display,Cow,gc,x1-1,y1-1,x1-1,y2 );
@@ -1959,7 +1959,7 @@ int CheckEndianess(void)
int i;
} ec;
- ec.i = 8;
+ ec.i = 8;
return (ec.b[0] == 0);
}
@@ -1983,7 +1983,7 @@ void initgui_(int *model, int *debug, int *lats, int *mrpid, int *mrnum, char *p
gettimeofday(&TimeVal,NULL);
Seed = TimeVal.tv_sec;
-
+
Model = *model;
Debug = *debug;
Latitudes = *lats;
@@ -2000,7 +2000,7 @@ void initgui_(int *model, int *debug, int *lats, int *mrpid, int *mrnum, char *p
if (Debug) printf("initgui(%d,%d)\n",Model,Debug);
if ((display=XOpenDisplay(display_name)) == NULL)
{
- fprintf(stderr,"%s: cannot connect to X server %s\n",
+ fprintf(stderr,"%s: cannot connect to X server %s\n",
progname, XDisplayName(display_name));
exit(1);
}
@@ -2063,7 +2063,7 @@ void initgui_(int *model, int *debug, int *lats, int *mrpid, int *mrnum, char *p
wm_hints.initial_state = NormalState;
wm_hints.input = True;
wm_hints.flags = StateHint | InputHint;
-
+
class_hints.res_name = progname;
class_hints.res_class = "PUMA";
@@ -2115,7 +2115,7 @@ void initgui_(int *model, int *debug, int *lats, int *mrpid, int *mrnum, char *p
for (i=0 ; i < NUMPAL ; ++i)
LineCo[i] = AllocateColorCells(Pallet[i]);
-
+
/* Color cells for control window */
XAllocNamedColor(display,colormap,"red" ,&Red ,&Dummy);
@@ -2646,7 +2646,7 @@ void LinePlot(int w)
}
// fill plot area with black
-
+
XSetBackground(display,gc,BlackPix);
XSetForeground(display,gc,BlackPix);
XFillRectangle(display,pix,gc,0,0,WinXSize,WinYSize);
@@ -2670,12 +2670,12 @@ void LinePlot(int w)
for (j=0 ; j < DimY ; ++j)
{
// scale plot data
-
+
for (i=0 ; i < DimX ; ++i)
{
LIxp[w][i].y = InYSize - f * (Field[i+j*DimX] - zmin);
}
-
+
XSetForeground(display,gc,Simplestrip[j].pixel);
XDrawLines(display,pix,gc,LIxp[w],DimX,CoordModeOrigin);
}
@@ -2952,7 +2952,7 @@ void TracerPlot(int w)
{
for (j=0 ; j < DimY; ++j)
{
- SpeedScale[j] = InXSize * DeltaTime * 60.0 / 40000000.0
+ SpeedScale[j] = InXSize * DeltaTime * 60.0 / 40000000.0
/ cos((j-0.5*(DimY-1)) * (M_PI/DimY));
}
SpeedScale[DimY-1] = SpeedScale[0] = SpeedScale[1];
@@ -3111,11 +3111,11 @@ void SH_Amplitudes(int w)
}
-/* ========== */
-/* Amplitudes */
-/* ========== */
+/* ============= */
+/* FC_Amplitudes */
+/* ============= */
-void Amplitudes(int w)
+void FC_Amplitudes(int w)
{
int i,j,m,n;
int x,y;
@@ -3155,14 +3155,17 @@ void Amplitudes(int w)
dx = WinXSize / (DimX+1);
dy = WinYSize / (DimY+1);
+ if (dx < dy) dy = dx;
+ else dx = dy;
r = (dx+dx+dy+dy) / 6;
XSetForeground(display,gc,BlackPix);
- for (m=0,i=0 ; m < DimX ; ++m)
+ i = 0;
+ for (n=0 ; n < DimY ; ++n)
{
- y = FixFontHeight + 4 + m * dx;
- for (n=0 ; n < DimY ; ++n)
+ y = FixFontHeight + 4 + n * dy;
+ for (m=0 ; m < DimX ; ++m)
{
- x = dx/2 + n * dx;
+ x = dx/2 + m * dx;
XSetForeground(display,gc,Aco[w][i++].pixel);
XFillArc(display,pix,gc,x,y,r,r,0,360*64);
}
@@ -3201,7 +3204,7 @@ void ReopenWindow(int i)
{
if (WinAtt[i].x < ScreenOffset) WinAtt[i].x = ScreenOffset + OutXSize * (i % WinCols);
if (WinAtt[i].y < ScreenOffset) WinAtt[i].y = ScreenOffset + OutYSize * (i / WinCols);
- Win[i] = XCreateSimpleWindow(display,RootWindow(display,screen_num),
+ Win[i] = XCreateSimpleWindow(display,RootWindow(display,screen_num),
WinAtt[i].x,WinAtt[i].y,WinAtt[i].w,WinAtt[i].h,
BorderWidth,BlackPix,WhitePix);
XSetWMProtocols(display,Win[i],&Delwin,1);
@@ -3265,7 +3268,7 @@ void DisplayHelpWindow(void)
h = BigFontHeight * (HelpLines + 1);
x = (ScreenW - w) / 2;
y = (ScreenH - h) / 2;
- HelpWindow = XCreateSimpleWindow(display,RootWindow(display,screen_num),
+ HelpWindow = XCreateSimpleWindow(display,RootWindow(display,screen_num),
x,y,w,h,BorderWidth,Yellow.pixel,DarkBlue.pixel);
XStringListToTextProperty(&HelpTitle,1,&HelpName);
XSetWMProtocols(display,HelpWindow,&Delwin,1);
@@ -3619,7 +3622,7 @@ void guiclose_(void)
}
while (!(XCheckTypedWindowEvent(display,Cow,ButtonPress,&CowEvent) &&
HitStopButton(&CowEvent)));
-
+
// XCloseDisplay(display); // segmentation fault on sun compiler!
}
@@ -3728,7 +3731,7 @@ void lp2ps(REAL *a, REAL *b)
{
dx = arx * (xnp - i);
dy = ary * (ynp - j);
- x = atan2(dx,dy) * lfa; // angle
+ x = atan2(dx,dy) * lfa; // angle
y = sqrt(dx * dx + dy * dy); // distance from NP
if (x < 0.0) x += (DimX-1);
k = x; // integer part
@@ -4028,23 +4031,23 @@ void ShowGridPolar(void)
XSetForeground(display,gc,WhitePix);
XSetBackground(display,gc,BlackPix);
XSetLineAttributes(display,gc,1,LineOnOffDash,CapButt,JoinRound);
-
+
/* Northern Hemisphere */
-
+
XDrawArc(display,pix,gc,OffX+dx/6,OffY+dy/6,2*dx/3,2*dy/3,0,360*64);
XDrawArc(display,pix,gc,OffX+dx/3,OffY+dy/3,dx/3,dy/3,0,360*64);
-
+
XDrawLine(display,pix,gc,OffX,yh,InXSize,yh);
XDrawLine(display,pix,gc,OffX+xh,OffY,OffX+xh,InYSize);
-
+
/* Southern Hemisphere */
-
+
XDrawArc(display,pix,gc,OffX+7*dx/6,OffY+dy/6,2*dx/3,2*dy/3,0,360*64);
XDrawArc(display,pix,gc,OffX+4*dx/3,OffY+dy/3,dx/3,dy/3,0,360*64);
-
+
x = OffX + dx + xh;
XDrawLine(display,pix,gc,x,OffY,x,InYSize);
-
+
if (GridLabel)
{
x = OffX + xh - FixFontWidth/2;
@@ -4206,7 +4209,7 @@ void iso(int w,int PicType,REAL *field,int dimx,int dimy,int dimz,int pal)
char Text[128];
int i,j,k,len,lens,xp,yp,status,x;
- int y,dx,r,width,height;
+ int y,dx,dy,r,width,height;
INTXU border,depth;
REAL f,o,ra,rb;
int CapLines;
@@ -4221,7 +4224,7 @@ void iso(int w,int PicType,REAL *field,int dimx,int dimy,int dimz,int pal)
// At high frame rates (SkipFreq > 1) some types are redrawn
// at "SkipFreq" intervals
- if (SkipFreq > 1 && (nstep % SkipFreq) != 0 &&
+ if (SkipFreq > 1 && (nstep % SkipFreq) != 0 &&
(PicType == ISOCS || PicType == ISOHOR ||
PicType == MAPHOR || PicType == ISOCOL ||
PicType == ISOREC )) return;
@@ -4436,12 +4439,12 @@ void iso(int w,int PicType,REAL *field,int dimx,int dimy,int dimz,int pal)
pix = WinPixMap[w].Pix; /* Set current pixmap */
/* Draw colour bar */
-
+
if ((SizeChanged || Cstrip == Autostrip) &&
(PicType == ISOCS || PicType == ISOHOR ||
- PicType == ISOHOV || PicType == ISOLON ||
+ PicType == ISOHOV || PicType == ISOLON ||
PicType == ISOCOL || PicType == MAPHOR ||
- PicType == ISOREC ))
+ PicType == ISOREC || PicType == ISOAMP))
{
XSetForeground(display,gc,BlackPix);
XFillRectangle(display,pix,gc,0,InYSize,WinXSize,WinYSize);
@@ -4489,7 +4492,7 @@ void iso(int w,int PicType,REAL *field,int dimx,int dimy,int dimz,int pal)
}
/* Draw mode legend */
-
+
if (SizeChanged && PicType == ISOSH)
{
dx = WinXSize / 23;
@@ -4552,6 +4555,73 @@ void iso(int w,int PicType,REAL *field,int dimx,int dimy,int dimz,int pal)
}
}
+ /* Double Fourier Coefficients */
+
+ if (SizeChanged && PicType == ISOAMP)
+ {
+ dx = WinXSize / (DimX+1);
+ dy = WinYSize / (DimY+1);
+ if (dx < dy) dy = dx;
+ else dx = dy;
+ XSetForeground(display,gc,BlackPix);
+ XFillRectangle(display,pix,gc,0,0,WinXSize,WinYSize);
+
+ XSetForeground(display,gc,LightGreen.pixel);
+ XSetBackground(display,gc,BlackPix);
+ for (i=0 ; i < DimX ; i+=2)
+ {
+ sprintf(Text,"%d",i);
+ len = strlen(Text);
+ width = XTextWidth(FixFont,Text,len);
+ height = FixFont->ascent + FixFont->descent;
+ xp = dx + i * dx - width/2 - FixFontWidth/2 + 1;
+ yp = FixFontHeight;
+ XDrawImageString(display,pix,gc,xp,yp,Text,len);
+ }
+ XSetForeground(display,gc,LightBlue.pixel);
+ for (i=0 ; i < DimY ; i+=2)
+ {
+ sprintf(Text,"%d",i);
+ len = strlen(Text);
+ width = XTextWidth(FixFont,Text,len);
+ height = FixFont->ascent + FixFont->descent;
+ xp = WinXSize - width - 2;
+ yp = 2 * FixFontHeight + i * dy;
+ if (yp+FixFont->descent > InYSize) break;
+ XDrawImageString(display,pix,gc,xp,yp,Text,len);
+ }
+ strcpy(Text,"n/m");
+ len = strlen(Text);
+ width = XTextWidth(FixFont,Text,len);
+ xp = WinXSize - width - 2;
+ yp = FixFontHeight;
+ XSetForeground(display,gc,WhitePix);
+ XDrawImageString(display,pix,gc,xp,yp,Text,len);
+ strcpy(Text,"High ");
+ len = strlen(Text);
+ width = XTextWidth(FixFont,Text,len);
+ xp = WinXSize/2 - AMPLI_COLS * 10 - width;
+ yp = WinYSize - FixFontHeight + 10;
+ r = FixFontHeight-2;
+ XSetForeground(display,gc,WhitePix);
+ if (xp > 0) XDrawImageString(display,pix,gc,xp,yp,Text,len);
+ strcpy(Text," Low");
+ len = strlen(Text);
+ width = XTextWidth(FixFont,Text,len);
+ xp = WinXSize/2 + AMPLI_COLS * 10;
+ if (xp + width < WinXSize) XDrawImageString(display,pix,gc,xp,yp,Text,len);
+ yp = InYSize;
+ XDrawLine(display,pix,gc,OffX,yp,WinXSize,yp);
+ yp = WinYSize - r - FixFont->descent;
+
+ for (i=0 ; i < AMPLI_COLS ; ++i)
+ {
+ xp = WinXSize/2 - AMPLI_COLS * 10 + i * 20;
+ XSetForeground(display,gc,AmpliStrip[AMPLI_COLS-i-1].pixel);
+ XFillArc(display,pix,gc,xp,yp,r,r,0,360*64);
+ }
+ }
+
if (SizeChanged && PicType == ISOTS) /* Timeseries Caption */
{
XSetForeground(display,gc,BlackPix);
@@ -4593,7 +4663,7 @@ void iso(int w,int PicType,REAL *field,int dimx,int dimy,int dimz,int pal)
XSetBackground(display,gc,BlackPix);
}
- if (PicType == ISOTS)
+ if (PicType == ISOTS)
{
if (TSxp[w] == NULL) TSxp[w] = SizeAlloc(DimX * DimY , sizeof(XPoint),"TSxp");
if (Dmin[w] == NULL) Dmin[w] = FloatAlloc(DimY ,"Dmin");
@@ -4621,7 +4691,7 @@ void iso(int w,int PicType,REAL *field,int dimx,int dimy,int dimz,int pal)
o = Dmin[w][j];
if ((Dmax[w][j] - Dmin[w][j]) > 1.0e-20) f = (InYSize-2) / (Dmax[w][j] - Dmin[w][j]);
else f = 1.0;
-
+
for (i=1 ; i < DimX ; ++i)
{
TSxp[w][i].x = VGAX * i;
@@ -4631,7 +4701,7 @@ void iso(int w,int PicType,REAL *field,int dimx,int dimy,int dimz,int pal)
}
}
- if (PicType == ISOTAB)
+ if (PicType == ISOTAB)
{
XSetForeground(display,gc,BlackPix);
XSetBackground(display,gc,BlackPix);
@@ -4783,26 +4853,26 @@ void iso(int w,int PicType,REAL *field,int dimx,int dimy,int dimz,int pal)
{
IsoAreas(Cstrip);
}
-
+
// amplitudes of coeeficients of spherical harmonics
if (PicType == ISOSH)
{
- SH_Amplitudes(w);
+ SH_Amplitudes(w);
}
// amplitudes of rectangular array
if (PicType == ISOAMP)
{
- Amplitudes(w);
+ FC_Amplitudes(w);
}
// line plot
if (PicType == LINE)
{
- LinePlot(w);
+ LinePlot(w);
}
if (Grid && PicType == ISOCS) ShowGridCS();